1. Have the Java Perspective open, so that Eclipse knows to interpret things in a Java context.
2. In the Explorer view, expand your file list until you see the Java source files you're interested in.
3. Right-click the mouse on the Java source file's name in the Explorer View. A menu should pop up, and one of the options should be "Run as...". Select Java Application to run the application. There's also a "Debug As..." menu option. It acts the same way, except that the class will run under the debugger.
If the class selected does not have a method defined that matches the signature for "public static void main(
String[] args)" the class is not executable according to Java's requirements and no action will be taken.
Also, use of the default package is a Bad Thing. Some things just won't work if they aren't in a non-default package. You can create a non-default package using Eclipse (either via the "New/Package" menu option or by creating directories under pn of your project's source directories). Then use the Explorer right-mouse "Move" feature to move the selected Java files into the package directory. Multiple files may be selected at once using the usual GUI conventions.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.